1 Answer
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Try putting spaces between the relation symbols, otherwise it will look like a malformed HTML tag. As in 0 < h(p) < 1 .

Oh, and I think it is not possible if h has integral coefficients and p also has integer parts.

EDIT: Upon rereading the problem, I see where it is possible that h could exist,
however, by scaling, I think it could turn into an undecidable variant of Hilbert's 10th:
deciding if 0 < h(p) < 1 may be the same as deciding if 2h(p) has a solution. END EDIT